I'm writing a horror story where a mad doctor skins a man and tosses him into a tank filled with compatible human blood. It has a breathing tube which is inserted into the mouth and a pump to bubble oxygen in the blood tank. How likely is the man to survive the ordeal? The setup is carefully monitored and free of contamination.
I see three issues, so whilst my answer is not full, I hope it is an answer.
Skinning might put him in shock condition. Circulatory shock is deadly. So this is first point of failure.
No blood is perfectly compatible, except his own. We go with "good enough" because we only use small amounts at a time. Substantial transfusions of best blood available are risky and may result with problems, sometimes death. And we are talking about up to seven liters. Your pool would be dozens or hundreds liters of blood.
Keeping blood fresh will be a major problem. His body can do it for his original 6 - 7 liters. Not for 100, no way. And you need to prevent coagulation. Remove carbon dioxide. I seriously doubt it is doable. For sure not as simple as bubbling. For some hours battery of cardiopulmonary bypasses would help. Of course, these would introduce their own problems to the system.
So no, what you described seems impossible with current state of medical knowledge.
TL;DR: It's complex and any chosen system will need constant and diligent care.
A few things. First, the skinning itself is physically traumatic. The pain alone could send a person into shock and can force the brain to shut down permanently (i.e. death). Second is potential bloodloss during the skinning, which could send the victim into shock, and eventually kill him. And last is infections slowly creeping up on the victim and killing him. So how to counter this?
The most troubling is the physical trauma of the skinning, but not something that cannot be worked around. Some sedatives beforehand could dull it enough that this is not impossible.
The bloodloss is probably why you would want to have the victim in the blood in the first place, which isn't a bad countermeasure. However, you negate Malots points of blood transfusion. This, too, can be worked around. There are hormones that can be used to beef up blood, or at worst just blood plasma which works around the blood transfusion problem entirely. It does require a lot more planning, but keeping the victim in blood plasma is probably the better choice.
Next comes the CO2 problem. This can be worked around with machines. There are machines used today that filter out CO2 and oxygenate the blood. In fact, you could shut down the victim's lungs entirely, and only have them on this machine. Yes, there are side-effects to this, and longterm usage is discouraged. So you may not want to go that route.
Human refuse problem. A stoma could deal with the majority of this, if combined with a catheter. However, both options are not eternally sterile. And even condom catheters (essentially what can be used in space to avoid those pesky bathroom hazards in 0G) need to be changed regularly.
Bacterial infection. Anything not originally of the human body that is inserted, risks rejection. The autoimmune system is usually equipped to deal with such things, but there are ways around this. The trouble comes when you face the most basic facts that you need to subdue this system to ensure the victim's body doesn't shut down from longterm trauma and/or atrophy (I would advise you look into comatose patient care for more details on this).
Bedsores. This is a silent killer, and even if the victim is kept submerged the risks don't disappear entirely. Why? Tubes pressing against the victim, anything rubbing against the exposed tissue (tubing, wiring, the container). Lack of skin doesn't solve this issue, because bedsores can and do go deeper than skin.
Long story short? There are more facets of long term medical care that need to be looked at than simply getting the victim to survive past the worst of it.
I think you have to add a sealed catheter to the guy, and a shit-tube, or else he will be living in his own excrement, which I don't imagine a person could long survive. He'll have to take vitamin d, because vitamin d is produced through the skin. Without the skin, I imagine he'll be a lot more prone to injury, since the skin cushions the insides somewhat. Molot raises a good point with keeping the blood fresh, but I see a couple of ways this could be done. Either the doctor produces it with stem cells/living bone marrow sample from the patient(a little sci-fi, but not too far off), or the tube is molded to the patient himself, and is just slightly larger than him, so not a huge amount of extra blood. As for CO2, It will bubble out(if the blood is exposed to the air at least occasionally. In fact, if you gave the blood enough surface area, you could let diffusion do all the work of providing oxygen, so he can't kill himself by taking off the mask.
He could survive cause the story requires him to do so. Even though you want the setting to be realistic, you can bend the rules a little for your story's purpose; besides, we already had a Dr.Moreau fusing peoples' and animals' parts together, or a Dr. Frankenstein animating a being made from cadavers' pieces.
The severing of all of the nerve paths to the majority of the skin embedded nerve endings would cause continuous pain, while on the other hand the majority of sensory apparatus would be missing. I don't know that the victim could ever attain consciousness without enduring so much pain as to send them into shock. Their are drugs that might mitigate the pain but such drugs tend to have other negative effects.
Assuming the doctor that did this is interested in having the victim actually realize the horror of his inevitably mortal plight, the drugs may work long enough to produce the desired hopelessness, but how would the victim learn what had happened to him? The victim could not see through the blood and would have no nerve endings in his hands to examine his situation. I suppose the doctor could communicate verbally what had been done but this seems insufficient to the story.